Bottleneck in multiphonon nonradiative transitions

Abstract

The nonradiative decay process of rare-earth ions in solids has been considered up to now to be independent of excitation intensity. In this paper we show that the multiphonon nonradiative decay probabilities of rare-earth ions in a germanate glass are reduced at high excitation state densities for the larger energy gaps. The classical exponential energy gap law is shown to 'rotate' at higher excitation around the 3.2-phonon point. The observed effect is described in terms of a spatial saturation of the accepting mode term with an effective diffusion length ranging between 45 and 20 \AA{} for excited state density from 2\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 8\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ at an active ion concentration of 2.5\ifmmode\times\else\texttimes\fi{}${10}^{19}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$.